While Harvest does not allow you to delete older versions while leaving newer versions in place, what you can do is demote those versions to a state that does not have a view assigned, and this will make them invisible to the other states.
In your project create a state named “TrashBin” and in the “View” field select “No View”. Leave the “All snapshot” checkbox unchecked.
Next, make sure that all your states have a “Demote” process that demotes back to the previous state. In your initial state, create a Demote process to demote to the TrashBin state. For all your demote processes make sure the “Enforce Package Bind” and “Verify Package Dependency” checkboxes are unchecked.
With these settings in place, you can now demote any packages back through all the states and then demote it into the Trash Bin state. Those packages and versions will no longer be visible from the other views.